The tension of a stretched string is increased by 69%. In order to keep its frequency of vibration constant, its length must be increased by :

Options

A. `40%`
B. `30%`
C. `20%`
D. `10%`

Answer

B

Explanation

Given : `T_(2)/T_(1) = 169/ 100 :' n_(1) = n_(2)`
` :. 1/(2L_(1)) sqrt(T_(1)/m) = 1/(2L_(2)) sqrt(T_(2)/m) `
` :. sqrt(T_(2)/T_(1) ) = L_(2)/L_(1) :. sqrt(169/100) = 13/10 = L_(2)/L_(1)`
` :. L_(2) = 1.3 L_(1) :. L_(2) - L_(1) = 0.3L_(1)`
` :. ((L_(2) - L_(1))/L_(1))xx 100 = (0.3L_(1))/L_(1) xx 100 = 30 %`